Second order nonlinear gyrokinetic theory : From the particle to the gyrocenter

Abstract

A gyrokinetic reduction is based on a specific ordering of the different small parameters characterizing the background magnetic field and the fluctuating electromagnetic fields. In this tutorial, we consider the following ordering of the small parameters: $\epsilon \_B=\epsilon \_{\delta }^2$ where $\epsilon \_B$ is the small parameter associated with spatial inhomogeneities of the background magnetic field and $\epsilon \_\delta$ characterizes the small amplitude of the fluctuating fields. In particular, we do not make any assumption on the amplitude of the background magnetic field. Given this choice of ordering, we describe a self-contained and systematic derivation which is particularly well suited for the gyrokinetic reduction, following a two-step procedure. We follow the approach developed in [Sugama, Physics of Plasmas 7, 466 (2000)]:In a first step, using a translation in velocity, we embed the transformation performed on the symplectic part of the gyrocentre reduction in the guiding-centre one. In a second step, using a canonical Lie transform, we eliminate the gyroangle dependence from the Hamiltonian. As a consequence, we explicitly derive the fully electromagnetic gyrokinetic equations at the second order in $\epsilon \_\delta$.

References in corpus (4)

• Second order Gyrokinetic theory for Particle-In-Cell codes
• The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems
• Hierarchy of second-order gyrokinetic Hamiltonian models for particle-in-cell codes
• Equivalence of two independent calculations of the higher order guiding center Lagrangian

Cited by in corpus (6)

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• First principles gyrokinetic analysis of electromagnetic plasma instabilities
• Implementation of energy transfer technique in ORB5 to study collisionless wave-particle interactions in phase-space
• Gyrokinetic theory with polynomial transforms: a model for ions and electrons in maximal ordering